Shape outlier detection and visualization for functional data: the outliergram

We propose a new method to visualize and detect shape outliers in samples of curves. In functional data analysis, we observe curves defined over a given real interval and shape outliers may be defined as those curves that exhibit a different shape from the rest of the sample. Whereas magnitude outliers, that is, curves that lie outside the range of the majority of the data, are in general easy to identify, shape outliers are often masked among the rest of the curves and thus difficult to detect. In this article, we exploit the relationship between two measures of depth for functional data to help to visualize curves in terms of shape and to develop an algorithm for shape outlier detection. We illustrate the use of the visualization tool, the outliergram, through several examples and analyze the performance of the algorithm on a simulation study. Finally, we apply our method to assess cluster quality in a real set of time course microarray data.